Feeding a low-iodine food can be as effective at treating hyperthyroidism as tablets, if used appropriately.
Iodine is used by the thyroid gland to produce thyroid hormone. By reducing the availability of iodine, the amount of thyroid hormone produced is reduced. Iodine is found in many food items, and is particularly high in canned food. A diet with extremely restricted levels of iodine (Hills y/d) has been available in the UK since 2011.
It must be fed exclusively, as supplementation with any other foodstuffs will provide iodine and render the diet useless. It is therefore most effective with indoor cats in single-cat households. In multi-cat households, it is possible to feed the unaffected cats on this diet, however they will need some regular food as well to provide some iodine. A microchip-controlled cat feeder is useful for multi-cat household where one or more cats needs a special diet as they restrict which cat can access which bowl.
As with any diet change, a transition period is important. If your cat is a particularly fussy eater, this may need to be extended. Gradually increase the amount of new food offered and reduce the amount of old food over a week or so as shown here.
As with anti-thyroid medication, regular monitoring of thyroid hormone levels by your vet is needed while your cat is on this diet, to ensure that the disease is well controlled.